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matching (Definition)

Let $ G$ be a graph. A matching $ M$ on $ G$ is a subset of the edges of $ G$ such that each vertex in $ G$ is incident with no more than one edge in $ M$.

It is easy to find a matching on a graph; for example, the empty set will always be a matching. Typically, the most interesting matchings are maximal matchings. A maximal matching on a graph $ G$ is simply a matching of the largest possible size.

A perfect matching is a matching that saturates every vertex.



"matching" is owned by Mathprof. [ full author list (2) | owner history (1) ]
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See Also: maximal matching/minimal edge covering theorem, matching, edge covering, saturate

Also defines:  maximal matching, perfect matching

Attachments:
maximal matching/minimal edge covering theorem (Theorem) by mps
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Cross-references: saturates, size, empty set, incident, vertex, edges, subset, graph
There are 25 references to this entry.

This is version 4 of matching, born on 2002-05-26, modified 2006-09-27.
Object id is 2939, canonical name is Matching.
Accessed 9158 times total.

Classification:
AMS MSC: 05C70 (Combinatorics :: Graph theory :: Factorization, matching, covering and packing)
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